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1986 IMO Longlists
63
63
Part of
1986 IMO Longlists
Problems
(1)
A'B', B'C', C'A intersects the incircle in two points
Source:
8/29/2010
Let
A
A
′
,
B
B
′
,
C
C
′
AA',BB', CC'
A
A
′
,
B
B
′
,
C
C
′
be the bisectors of the angles of a triangle
A
B
C
(
A
′
∈
B
C
,
B
′
∈
C
A
,
C
′
∈
A
B
)
ABC \ (A' \in BC, B' \in CA, C' \in AB)
A
BC
(
A
′
∈
BC
,
B
′
∈
C
A
,
C
′
∈
A
B
)
. Prove that each of the lines
A
′
B
′
,
B
′
C
′
,
C
′
A
′
A'B', B'C', C'A'
A
′
B
′
,
B
′
C
′
,
C
′
A
′
intersects the incircle in two points.
geometry
geometric transformation
reflection
geometry unsolved